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Article Dans Une Revue Journal of the European Mathematical Society Année : 2023

On degenerate blow-up profiles for the subcritical semilinear heat equation

Frank Merle
  • Fonction : Auteur
Hatem Zaag

Résumé

We consider the semilinear heat equation with a superlinear power nonlinearity in the Sobolev subcritical range. We construct a solution which blows up in finite time only at the origin, with a completely new blow-up profile, which is cross-shaped. Our method is general and extends to the construction of other solutions blowing up only at the origin, with a large variety of blow-up profiles, degenerate or not.

Dates et versions

hal-03873073 , version 1 (26-11-2022)

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Frank Merle, Hatem Zaag. On degenerate blow-up profiles for the subcritical semilinear heat equation. Journal of the European Mathematical Society, In press. ⟨hal-03873073⟩
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